In order to divide $306 into the ratio of 9 to 5 to 3, first you have to make each section of the ratio represented by a variable, and put it into an equation.
9x + 5x + 3x = 306
Our next step is to simplify the left side of the equation by combining all of the like terms, the ones that contain variables.
17x = 306
Finally, to solve this equation, you have to divide both sides by 17 to isolate the variable x on the left side of the equation.
x = 18
However, this is not our answer as it isn't in a ratio format and doesn't really make sense. To find our ratio, we have to multiply each of our initial numbers (9, 5, and 3) by our variable, x.
9 * 18 = 162
5 * 18 = 90
3 * 18 = 54
You can verify that these numbers are correct because if you add them together you get 306.
Your final ratio is 162:90:54.
Hope this helps! :)
If you have a separate specific question about pre-tax prices and PMed me the link, I'd be happy to help you.
Answer: 691
<u>Step-by-step explanation:</u>
There are 3 different ways to find the remainder. I am not sure which method you are supposed to use, so I will solve using all 3 methods.
Long Division:
<u> 10x³ + 24x² + 77x + 230 </u>
x - 3 ) 10x⁴ - 6x³ + 5x² - x + 1
- <u>(10x⁴ - 30x³) </u> ↓ ↓ ↓
24x³ + 5x² ↓ ↓
- <u>(24x³ - 72x²) </u> ↓ ↓
77x² - x ↓
- <u>(77x² - 231x) </u> ↓
230x + 1
- <u>(230x - 690)</u>
691 ← remainder
Synthetic Division:
x - 3 = 0 ⇒ x = 3
3 | 10 -6 5 -1 1
|<u> ↓ 30 72 231 690</u>
10 24 77 230 691 ← remainder
Remainder Theorem:
f(x) = 10x⁴ - 6x³ + 5x² - x + 1
f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3) + 1
= 810 - 162 + 45 - 3 + 1
= 691
Answer:
B. (3, 0), (0, -6)
Step-by-step explanation:
Plug 0 in for each variable one at a time, and you will get both intercepts.
Answer:
Case n =5
Case n =15
Case n = 40
P value
Case n =5
Case n =15
Case n =40
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 5, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Case n =5
Case n =15
Case n = 40
P-value
Since is a left tailed test the p value would be:
Case n =5
Case n =15
Case n =40
Answer:
Step-by-step explanation:
To find which one is prime, let's try to factor them all. We can use the factoring by grouping method.
and
and
So this one is not prime, since you can still factor it.
and
and
So this one is not prime, since you can still factor it.
and
and
So this one is not prime, since you can still factor it.
and
and -x+2 cannot be further factored.
Therefore, is a prime.
